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Mirrors > Home > ILE Home > Th. List > Mathboxes > strcollnft | Unicode version |
Description: Closed form of strcollnf 13183. Version of ax-strcoll 13180 with one disjoint variable condition removed, the other disjoint variable condition replaced with a non-freeness antecedent, and without initial universal quantifier. (Contributed by BJ, 21-Oct-2019.) |
Ref | Expression |
---|---|
strcollnft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strcoll2 13181 | . 2 | |
2 | nfnf1 1523 | . . . . 5 | |
3 | 2 | nfal 1555 | . . . 4 |
4 | 3 | nfal 1555 | . . 3 |
5 | nfa2 1558 | . . . 4 | |
6 | nfvd 1509 | . . . . 5 | |
7 | nfa1 1521 | . . . . . . . 8 | |
8 | nfcvd 2282 | . . . . . . . 8 | |
9 | sp 1488 | . . . . . . . 8 | |
10 | 7, 8, 9 | nfrexdxy 2468 | . . . . . . 7 |
11 | 10 | sps 1517 | . . . . . 6 |
12 | 11 | alcoms 1452 | . . . . 5 |
13 | 6, 12 | nfbid 1567 | . . . 4 |
14 | 5, 13 | nfald 1733 | . . 3 |
15 | nfv 1508 | . . . . . 6 | |
16 | 5, 15 | nfan 1544 | . . . . 5 |
17 | elequ2 1691 | . . . . . . 7 | |
18 | 17 | adantl 275 | . . . . . 6 |
19 | 18 | bibi1d 232 | . . . . 5 |
20 | 16, 19 | albid 1594 | . . . 4 |
21 | 20 | ex 114 | . . 3 |
22 | 4, 14, 21 | cbvexd 1899 | . 2 |
23 | 1, 22 | syl5ib 153 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wnf 1436 wex 1468 wral 2416 wrex 2417 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-strcoll 13180 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 |
This theorem is referenced by: strcollnf 13183 |
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